Question:
Jennifer can finish a work in 6 days. Linda can finish the same work in 7 days while Elizabeth can finish the work in 8 days. How long will it take to finish it if they work together?
Correct Answer
2 22/73 days or 2.301 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jennifer = 6 days
And, the number of days required to finish the same work by Linda = 7 days
And, the number of days required to finish the same work by Elizabeth = 8 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 6 days the work is done by Jennifer = 1
∴ The work done by Jennifer in 1 day = 1/6
Similarly,
∵ In 7 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/7
Similarly,
∵ In 8 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/8 part
Now, the work done by Jennifer, Linda, and Elizabeth together in 1 day
= Jennifer's 1 day work + Linda's 1 day work + Elizabeth's 1 day work
= 1/6 + 1/7 + 1/8
= 28 + 24 + 21/168
= 73/168 part of work
This means in 1 day, 73/168 part of work is done by Jennifer, Linda and Elizabeth working together.
Now, the number of days required to finish 73/168 part of work by Jennifer, Linda, and Elizabeth working together = 1
∴ the number of days required to finish the whole work (1 work) by Jennifer + Linda + Elizabeth together
= 1/73/168
= 1 × 168/73 = 168/73 days
= 2 22/73 days = or 2.301 days
Thus, Jennifer, Linda, and Elizabeth working together will finish the total work (1 work) in 2 22/73 days = or 2.301 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Jennifer = 6 days
And the number of days required to finish the same work by Linda = 7 days
And the number of days required to finish the work by Elizabeth = 8 days
Thus, the number of days required to finish the work by Jennifer, Linda, and Elizabeth together = ?
Here a = 6 days
And, b = 7 days
And, c = 8 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jennifer, Linda, and Elizabeth working together
= 6 × 7 × 8/6 × 7 + 6 × 8 + 7 × 8 days
= 336/42 + 48 + 56 days
= 336/146 days
= 336/146 days
= 336 ÷ 2/146 ÷ 2 = 168/73 days
= 2 22/73 days or 2.301
Thus, Jennifer, Linda, and Elizabeth together will finish the work in 2 22/73 days or 2.301 days Answer
Similar Questions
(1) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?
(2) If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?
(3) James can finish a work in 5 days. John can finish the same work in 10 days while Michael can finish the work in 15 days. How long will it take to finish it if they work together?
(4) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?
(5) If David can finish the work in 32 days and Christopher can finish the same work in 48 days, then in how many days both can finish the work together?
(6) If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?
(7) Edward can finish a work in 57 days. Jeffrey can finish the same work in 62 days while Ryan can finish the work in 67 days. How long will it take to finish it if they work together?
(8) If Michael can finish the work in 30 days and Thomas can finish the same work in 46 days, then in how many days both can finish the work together?
(9) If Paul can finish the work in 36 days and Larry can finish the same work in 39 days, then in how many days both can finish the work together?
(10) Linda can finish a work in 12 days. Barbara can finish the same work in 17 days while Susan can finish the work in 22 days. How long will it take to finish it if they work together?